On Cerebral Hemodynamics: A Wave-Mechanical Analysis of Arterial Pressure, Flow Angle, and Perfusion Dynamics

Cerebral perfusion under hypertensive conditions presents paradoxes not fully explained by conventional pressure-flow models. This manuscript introduces a wavemechanical framework derived from the de Broglie relation (λp = h), establishing adual-pressure system with longitudinal pressure P_l = (1/2)ρ(v^2) cos^2 θ and transverse pressure P_t = 1/2ρ(v^2) sin^2 θ, where θ is the local flow angle and density ρ = δm/(δψ)^3 emerges from wave compaction geometry. The coupling pressure PT =1/2ρ(v^2) sinθ cosθ governs perfusion into arterial branches. As mean arterial pressure (MAP) increases, flow becomes predominantly longitudinal (θ → 0), leading to collapse of transverse pressure and impaired branch perfusion—despite rising global cerebral blood volume (CBV). This mechanism explains the paradoxical ischemic MRI patterns observed in hypertensive encephalopathy, where cortical vessels remain spared while deep and superficial perforators sustain injury. By modeling perfusion as wave energy transduction across vascular manifolds, this framework provides a novel structural lens on autoregulatory failure, perfusion collapse, and regional vulnerability.